Monadicity conjecture for the point functor on eventually coconnective affine DG schemes

Let $Z$ be an affine DG scheme locally almost of finite type, let $\iota:\operatorname{pt}\to Z$ be a point with image $z$, and consider the adjoint pair

$$\iota_*:\operatorname{Vect}\rightleftarrows \operatorname{QCoh}(Z)_{\{z\}}:\iota^{\operatorname{QCoh},!}.$$

Monadicity conjecture. If $Z$ is eventually coconnective, then the functor $\iota^{\operatorname{QCoh},!}$ is monadic. The paper states this as a conjectural assertion in the study of infinitesimal loop spaces; no resolution is supplied.